Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | #568×D53 |
| Fitting | C53×#568 ⋊ C2 |
| Sylow | C53 ⋊ C2×#568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D53 |
| commutator, socle | C2×C53 | C24×C4 |
| Fitting | C53×#568 | C2 |
| hypercenter | #568 | D53 |
| hypocenter | C53 | C2×#568 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1460 conjugacy classes of subgroups.
952 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1858, #27384936, D53×#1861, … |
| maximal normal subgroup of | D53×#1858, #27384936, D53×#1861, … |
| maximal quotient of | D53×#2873, D53×#2875, #568×Dic53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19217);